2016/03/08 by Mrinal K. Ghosh, Kuldeep Kumar, Ghosh, Mrinal K. +5
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Mathematics #Game Theory and Applications #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Simulation Techniques and Applications #Stochastic processes and financial applications #math.OC
paper · pdf · doi:10.48550/arxiv.1603.02454
arxiv created 2016/03/08 · openalex publication_date 2016/03/08 · arxiv updated 2016/03/09 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28
We study nonzero-sum stochastic games for continuous time Markov chains on a denumerable state space with risk sensitive discounted and ergodic cost criteria. For the discounted cost criterion we first show that the corresponding system of coupled HJB equations has an appropriate solution. Then under an additional additive structure on the transition rate matrix and payoff functions, we establish the existence of a Nash equilibrium in Markov strategies. For the ergodic cost criterion we assume a Lyapunov type stability assumption and a small cost condition. Under these assumptions we show that the corresponding system of coupled HJB equations admits a solution which leads to the existence of Nash equilibrium in stationary strategies.